Home
Class 12
MATHS
If two fair dices are thrown and digits ...

If two fair dices are thrown and digits on dices are a and b, then find the probability for which `omega^(ab) = 1`, (where `omega` is a cube root of unity).

Text Solution

Verified by Experts

The correct Answer is:
`(5)/(9)`
Total number of cases n(S) = 36
Since `omega^(ab)` = 1, ab must be multiple of 3.
So, at least one of a and b must be multiple of 3.
If none of the dices shows 3 or 6, number of cases is `4 xx 4 = 16`.
So, number of cases in which at least one of the dices shows 3 or 6 is 36 - 16 = 20.
`therefore` Required probability = `(20)/(36) = (5)/(9)`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • PROBABILITY I

    CENGAGE|Exercise Exercise 9.3|7 Videos

  • PROBABILITY I

    CENGAGE|Exercise Exercise (Single)|46 Videos

  • PROBABILITY I

    CENGAGE|Exercise Exercise 9.1|6 Videos

  • PROBABILITY AND STATISTICS

    CENGAGE|Exercise Question Bank|24 Videos

  • PROBABILITY II

    CENGAGE|Exercise JEE Advanced Previous Year|25 Videos

Similar Questions

Explore conceptually related problems

If a dice is thrown twice, then find the probability of getting 1 in the first throw only.

Four fair dices are thrown simultaneously. Find the probability that the highest number obtained is 4.

Knowledge Check

  • If two dice are thrown simultaneously, then the probability that the sum of the numbers which come up on the dice to be more than 5 is

    A
    `(5)/(36)`
    B
    `(1)/(6)`
    C
    `(5)/(18)`
    D
    `(13)/(18)`

  • Two dice are thrown simultaneously. Then the probability of getting two odd numbers is

    A
    `(1)/(6)`
    B
    `(2)/(6)`
    C
    `(7)/(36)`
    D
    `(1)/(4)`

    • Similar Questions

    Explore conceptually related problems

    Find the probability of getting more than 7 when two dice are rolled.

    Three dice are thrown simultaneously . Find the probability of getting the same number.

    If x=omega-omega^2-2 then , the value of x^4+3x^3+2x^2-11x-6 is (where omega is a imaginary cube root of unity)

    Three faces of a fair dice are yellow, two are red and one is blue. Find the probability that the dice shows (a) yellow, (b) red and (c ) blue face.

    A pair of dice is thrown 4 times. If getting a doublet is considered a success, find the probability of two successes.

    A fair dice is thrown three times. If p, q and r are the numbers obtained on the dice, then find the probability that i^(p) + i^(q) + i^(r) = 1 , where I = sqrt(-1) .

    Home
    Profile